How can I make ELIZA more realistic?
One 'easy' way would be to have some sort of conversational memory, where you track what the user has said already. I don't know how complex your patterns are, but if you could recognise names and track references, you could try and build up a mental model of the user's relationships with other people, and perhaps refer to that in your bots responses.

The latter will be quite advanced, but keeping track of things said earlier and referring back to them on occasion might make it appear a lot more capable.

As an added bonus, track changes in the user's sentiment scores, and see if you spot a pattern in the conversation (maybe over the course of multiple conversations) to see which bot utterance have the biggest (positive or negative) effect on the user's mood.